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Quantum Randomness

americanscientist.org

54 pointsTomte21 comments

Enjoyed the shout-out to Bohmian mechanics. Nonlocality may be weird, but you know what else is weird? Everything else about quantum mechanics. I'd actually prefer a nonlocal deterministic theory to a local indeterministic one, though I know that's just a philosophical preference. Still, I wish Bohmian mechanics was more popular; I wasn't even aware it existed until recently.

Multiverse is perfectly deterministic without all the issues with Bell's Inequality and needing a superfluous particle in addition to the wavefunction. I think pilot wave is throwing the baby out with the bathwater.

Pure randomness doesn't need physicality. The expansion of Omega, Chaitin's constant, is random. There is no model, program, or equation, that can predict the next bit.

Perhaps its possible the universe could be run on a cellular automata that is unpredictable in the same way. Is say, radioactive decay, truly random, or just can't be predicted by any program shorter than the underlying cellular automata process itself.

The fact that we can model the universe at all and predict parts of it at various scales -- that math works at all for physics -- is either remarkable, or perhaps required in any universe capable of intelligent life. :) Perhaps in a universe that is incomprehensible otherwise, evolution would not select for intelligence.

That's referenced in the article -- Chaitin's constant is 'algorithmically incompressible' according to Kolmogorov complexity -- though note that this definition means it's "assymptotically" random, but the first n bits can be approximated in finite time (there are other numbers with more strict randomness). What the article addresses is that if you're given a long string with that property you can't verify the randomness, by definition. But using the CHSH method outlined you can, assuming only some physical principles -- provided you're given a small 'seed' to start.

Note that the underlying "way" that the universe generates randomness doesn't matter from a scientific standpoint -- as long as we can't predict it, you can think of it as being generated by either an enormous computer or truly random (whatever that means).

About 3/4 of the way down, in response to: "The central idea in all of these protocols is simply to be stingy with the use of randomness. We ask Alice and Bob to play the CHSH game over and over again. However, in almost all of the plays, they simply both receive red cards—leading to a boring but also “cheap” (in terms of randomness) game. Only for a few randomly chosen plays does one of them receive a blue card."

If this is true, then these "clever" protocols are breaking the 50/50 rule of the CHSH game. Right?

Yes. In the normal CHSH game, the questions to the players Alice and Bob are independent random bits (50/50, as you say). That's a problem, though, if you want to create new randomness, because you put into the game two random bits and you get out less than two random bits! If you want to get out more randomness than you put in, you need to be a little more clever and more stingy with using random bits.

(If the players are honest, the first player's output is uniformly random, but the second player's output is ~85% predictable given the first player's output. Measured in terms of entropy, this means you are getting a fraction more than 1 bit out.)

The standard 50/50 CHSH is still useful for generating randomness, though. Even though it uses up more randomness than it creates, the output randomness can be of higher quality than the input randomness. More precisely, if the input bits are independent to the players Alice and Bob, but perhaps are known to an outside adversary, the game's output bits will be unknown to the adversary.

It is interesting to see how outcomes of the CHSH game to generate random bits. However, I am left wondering how Alice, Bob, or an external observer learns about the outcomes of the game?

Or, maybe I am misunderstanding the mechanics itself.

The idea of infinite randomness expansion really fascinates me, it's like watching Münchhausen pulling himself out of the swamp by his own hair.

How exactly do Alice and Bob use entangled electrons to win CHSH game with higher than 75% probability?

This may not answer your question, but you might enjoy seeing how the 85.4% probability is derived in http://arxiv.org/pdf/1209.0448v1.pdf and http://arxiv.org/pdf/1209.0449v1.pdf

A note -- if you're linking to arXiv, it's better to link to the abstract (http://arxiv.org/abs/1209.0448, http://arxiv.org/abs/1209.0449) rather than directly to the PDF. From the abstract, one can easily click through to the PDF; not so the reverse. And the abstract allows one to do things like see different versions of the paper, search for other things by the same authors, etc.

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